An Alternating Manifold Proximal Gradient Method for Sparse Principal Component Analysis and Sparse Canonical Correlation Analysis
An Alternating Manifold Proximal Gradient Method for Sparse Principal Component Analysis and Sparse Canonical Correlation Analysis
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DOI：
10.1287/ijoo.2019.0032
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发表时间：
2020-07
期刊：
影响因子：
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通讯作者：
Shixiang Chen;Shiqian Ma;Lingzhou Xue;H. Zou
中科院分区：
文献类型：
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作者：
Shixiang Chen;Shiqian Ma;Lingzhou Xue;H. Zou
稀疏主成分分析和稀疏典型相关分析是高维统计学和机器学习中用于分析大规模数据的两种基本技术。这两个问题都可以表述为一个具有非光滑目标和非凸约束的优化问题。由于非光滑性和非凸性给数值计算带来困难，文献中提出的大多数算法要么解决了其中的一些松弛问题，要么是启发式的，缺乏收敛性保证。在本文中，我们提出了一个新的交替流形近似梯度方法来解决这两个高维问题，并提供了一个统一的收敛性分析。数值实验结果证明了我们的算法的优点。
Sparse principal component analysis and sparse canonical correlation analysis are two essential techniques from high-dimensional statistics and machine learning for analyzing large-scale data. Both problems can be formulated as an optimization problem with nonsmooth objective and nonconvex constraints. Because nonsmoothness and nonconvexity bring numerical difficulties, most algorithms suggested in the literature either solve some relaxations of them or are heuristic and lack convergence guarantees. In this paper, we propose a new alternating manifold proximal gradient method to solve these two high-dimensional problems and provide a unified convergence analysis. Numerical experimental results are reported to demonstrate the advantages of our algorithm.